I do not know if this question fits this stack but I do not know if there's other place where I can ask.
The question is about the difference between the cooperative/collaborative radar system when localization a target. For the papers and textbooks I studied, I find they all use the CRLB (cramér–rao lower bound, the inverse of Fisher information matrix) to describe the performance of the radar localization minimize mean-squared error, and for the calculation is like something that: $\frac{\sigma^2}{\sum(\frac{\partial ln \textbf{p}(z|p)}{\partial p})^2}$.It is the sum of the likelihood function from each radar received echo.
And if I calculate the likelihood for each radar p$(z_i|p)$ ($i$ is the index of radar), and then times them together to get the total likelihood $\textbf{p}(z|p) = \prod \textbf{p}(z_i|p)$, I can also get a value which can be used to show the performance of the radar localization.
I wonder why the papers and books prefer the previous one not the second one, and how to understand the relationship between CRLB and likelihood function. Thank you.